Five Problems for Quantificational Semantics for Deontic and Bouletic Modality

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1 Five Problems for Quantificational Semantics for Deontic and Bouletic Modality The five problems: February 19, 2014 (1) Gradability of deontic modals and desire verb (2) Deontic and bouletic modals are not upward monotonic (3) Fine-grained interactions with probability (4) Deontic and bouletic comparatives (5) Deontic conflicts These are problems which arise for any quantificational semantics for expressions of desire, needs, and requirements. Lassiter distinguishes between two such types of quantificational semantics: Ideal-Worlds Semantics and Best-Available-Worlds Semantics. In Ideal-Worlds Semantics, context determines a set of accessible worlds, and then we quantify over this set using,, and. Let Deo be a function from worlds w and contexts c to the set of deontically accessible worlds from w in c and Boul be its bouletic counterpart. Then, (6) a. You ought to do your homework M,w = 1 if and only if: w Deo(c)(w) : You do your homework M,w = 1 b. You may have a piece of candy M,w = 1 if and only if: w Deo(c)(w) : You have a piece of candy M,w = 1 c. I want to go to Disneyland M,w = 1 if and only if: w Boul(c)(w) : I go to Disneyland M,w = 1 Recall from Kratzer (1991) that conditionals raise a problem for Ideal-World Semantics. (7) a. Charlie does not steal. b. If Charlie steals, he is punished. Taking if to denote the material conditional, (7b) is vacuously true since the antecedent will be false in all deontically accessible worlds. One way to solve this is to let Deo and Boul be functions from worlds w and contexts c to preference orders, rather than sets. Conditionals can then be treated by having the antecedent function as a restrictor on the modal ordering. For example, (8) If φ then ought ψ M,w h = ought ψ M,w h, where a. For all w, hw is the relevant deontic ordering on worlds. b. For all w, h (w) = df h(w) {w φ M,w,g,c = 1}. c. R A is the restriction of the binary order R to the set A. In general, semantics for deontic and bouletic modals in which they are interpreted as universal or existential quantifiers with restrictions are Best-Available-Worlds semantics. 1 Problem 1: Gradability of deontic modals and desire verb Deontic modals and desire verbs can occur with degree modification. (9) Ought: A war between Great Britain and the US ought very much to be deprecated. 1

2 (10) Should: I don t think he [UFC fighter Phil Davis] should be compared to Rosholt as much as he should be to Houston Alexander. (11) Require: The members of a literary group are required to have a blazer, more than they are required to have ever actually read the book. (12) Want: I am an American and I want very much to travel to Cuba. (13) Need: But really s need to be timely more than they need to be amazing. (14) Good: It is better for children to grow up in the countryside than in the big city. The data in (9)-(14) are problematic for a quantificational theory because quantifiers are not gradable, nor do they make reference to degrees or binary orders. We saw a related problem in von Fintel and Iatridou (2008): ought and should are weaker than must and have to. (15) a. You ought to wash your hands, but I guess I can t say you have to. b. # You have to wash your hands, but I guess I can t say you ought to. Kratzer s theory does not allow for such a distinction, but we saw that von Fintel and Iatridou can handle it by adding a second ordering source. However, von Fintel and Iatridou s account cannot explain the fact that ought and should participate in neg-raising while must and have to do not, as pointed out by Horn (1989). In this respect, ought and should pattern with most and relative-standard adjectives, while must and have to pattern with universal quantifiers and maximum-standard adjectives. (16) Ought, should, most and relative-standard adjectives a. I don t think you ought to leave. I think you ought to stay. b. I don t think most of my friends would like this music. I think most of my friends would dislike this music. c. I don t think Mary is happy. I think Mary is unhappy. (17) Must, have to, universal quantifiers, and maximum-standard adjectives. a. I don t think Sam must wash the dishes. I think Sam must not wash the dishes. b. I don t think Mary ate all the cookies. I think that Mary ate none of the cookies. c. I don t think the glass is full. I think the glass is empty. 2 Problem 2: Deontic and bouletic modals are not upward monotonic. (18) An operator O is upward monotonic iff df [φ ψ] = [O(φ) O(ψ)]. Both and are upward monotonic, which has the consequence that the following inferences involving conjunction and disjunction are valid. (19) Conjunction a. x[p (x) Q(x)] = x[p (x)] b. x[p (x) Q(x)] = x[p (x)] (20) Disjunction a. x[p (x)] = x[p (x) Q(x)] b. x[p (x)] = x[p (x) Q(x)] This predicts, correctly, that the following inferences are valid. 2

3 (21) a. A friend of mine lives in Houston and has a cat. So, a friend of mine lives in Houston. b. Everybody knows bill and everybody hates Fred. So, everybody knows Bill. (22) a. Some employee is in Atlanta. So, some employee is in Atlanta or Pittsburgh. b. All of the boys are in Atlanta. So, all of the boys are in Atlanta or Pittsburgh. There is a third valid inference, which holds only for the universal quantifier. (23) a. x[p (x)] x[q(x)] = x[p (x) Q(x)] b. Everybody has a cat, and everybody has a dog. So, everybody has a cat and a dog. For many deontic and bouletic modals D, these inferences are not valid. 2.1 Professor Procrastinate (D(φ ψ) = D(φ)) Jackson and Pargetter (1986): Prof. Procrastinate is invited to review a book on which he is the only fully qualified specialist on the planet. Procrastinate s notable flaw, however, is his inability to bring projects to completion. In particular, if Procrastinate accepts to review the book, it is extremely likely that he will not end up writing the review. In the eyes of the editor, and of the whole scientific community, this is the worst possible outcome. If Procrastinate declines, someone else will write the review someone less qualified than him, but more reliable. In this situation, it seems reasonable to judge (24a) true, but not (24b) false. (24) a. Prof. Procrastinate ought to accept and write the review. b. Prof. Procrastinate ought to accept. 2.2 Ross Paradox (D(φ) = D(φ ψ)) Ross (1944): (25) a. The boss wants you to go to Atlanta. So, the boss wants you to go to Atlanta or Boston. b. Mary needs to work harder. So, Mary needs to work harder or quit her job. c. We are required to drive less than 70mph. So, we are required to drive less than 70mph or more than 100mph. d. You should wash the dishes. So, you should wash the dishes or break them. It might seem plausible to rule these inferences out via Grice s Maxim of Quantity. But there are situations that suggest pragmatics are not at play here, including downward-entailing contexts and certain retractions (Cariani 2013). (26) a. I doubt that Lynn ought to either wear a tie or a scarf. In fact, I m reasonably certain she ought to wear a scarf. b. # I doubt that everyone is either Italian or French. In fact, I m reasonably certain that everyone is Italian. (27) a. Sam: According to the rules, you have to follow suit or play the king of trumps. Joan: No, the rules quite explicitly say you ought to follow suit, no matter what. Sam: I guess what I said was wrong. b. Sam: Everyone followed suit or played the king of trumps. Joan: Nobody had the king of trumps. Everyone followed suit. Sam: # I guess what I said was wrong. 3

4 2.3 Chicken (D(φ) D(ψ) = D(φ ψ)) Jackson (1985): Attila and Genghis are driving their chariots towards each other. If neither swerves, there will be a collision; if both swerve, there will be a worse collision (in a different place, of course); but if one swerves and the other does not, there will be no collision. Moreover if one swerves, the other will not because neither wants a collision. Unfortunately, it is also true to an even greater extent that neither wants to be chicken; as a result what actually happens is that neither swerves and there is a collision. In this situation, all of the following are intuitively true. (28) a. Attila ought to swerve. b. Genghis ought to swerve. c. It s not the case that Attila and Genghis ought to both swerve. 3 Fine-grained interactions with probability The problems in the last section seem to be related to probability. For example, Prof. Procrastinate ought to accept is false, even though in the best possible world he accepts and writes the review, because there is a high probability that if he accepts, he will not write the review. Consider a case of a doctor who must choose whether to treat a patient with medicine A or medicine B. A has a small chance of producing a cure and a larger chance of killing the patient. B will save the patient s life, although it will leave him slightly debilitated. The intuitive answer is that the doctor should choose B, since A is very risky. However, standard quantificational semantics says the doctor should choose A since every possible world is dominated by one in which the doctor gives the patient medicine A (and the patient lives). Or consider the Miner s Paradox. Kolodny and MacFarlane (2010): Ten miners are trapped either in shaft A or in shaft B, but we do not know which. Flood waters threaten to flood the shafts. We have enough sandbags to block one shaft, but not both. If we block one shaft, all the water will go into the other shaft, killing any miners inside it. If we block neither shaft, both shafts will fill halfway with water, and just one miner, the lowsest in the shaft, will be killed. We take it as obvious that the outcome of our deliberation should be (29) We ought to block neither shaft. Still, in deliberating about what to do, it seems natural to accept (30) If the miners are in shaft A, we ought to block shaft A. (31) If the miners are in shaft B, we ought to block shaft B. We also accept (32) Either the miners are in shaft A or they are in shaft B. But (30), (31), and (32) seem to entail (33) Either we ought to block shaft A or we ought to block shaft B. 4

5 And this is incompatible with (29). So we have a paradox. A Best-Available-Worlds Semantics gives us the truth of (30) and (31), since the antecedent of the if clause restricts us to worlds where the miners are in shaft A (30) or shaft B (31). However, it cannot give us (29) because in the unrestricted order, all worlds where we block neither shaft (and nine miners are saved) are strictly dominated by wolds in which we block one of the shafts (and ten miners are saved). Note that what we intuitively ought to do is not what we do in the best possible worlds. It is sub-optimal, but safe. Kolodny and MacFarlane try to salvage the quantificational semantics with what they call serious information-dependence. (34) A deontic selection function d is seriously information-dependent iff for some information states i 1, i 2 i 1, there is a world w i 2 such that w d(i 1 ) but w d(i 2 ). In other words, gaining information can reverse the deontic orderings between pairs of worlds. This makes it possible for all of (29)-(33) logically compatible. However, there are problems with this approach, as pointed out by Charlow (2013): i. Kolodny and MacFarlane cannot explain why (29) is intuitively true, they only show that it can be made consistent with (30)-(33). In principle, their fix allows information to affect the deontic ordering in any arbitrary way. ii. iii. Serious information-dependence means allowing information gain to reverse preferences among fullyspecified states of affairs. Charlow writes, If a possibility has enough (with respect to other possibilities in a set p) good-making features, then it does not cease having enough good-making features with respect to a contraction of p. Kolodny and MacFarlane justify serious information-dependence based on the intuition that a world in which both shafts are left open may be more ideal than one in which shaft A is closed relative to a less informed state, but less ideal relative to a more informed state. However, the intuition is actually about the ideality of propositions, not worlds. Worlds are fully-specified states of affairs. The ideality of a world in which both shafts are left open as compared to one where shaft A is closed depends on whether or not the miners are in shaft A, not on our information state. But intuitively, the ideality of the propositions to leave both shafts open or close shaft A does depend on our information state.s 4 Deontic and bouletic comparatives We can modify Kratzer s theory to make it resemble a degree semantics by identifying the degrees with equivalence classes of propositions under Kratzer s order. (35) s g(w) = {(p, q) w q w p : w g(w) w } The order over propositions in (35) is derived from the order over worlds. (36) g(w) = {(w, w ) {p : p g(w) w p} {q : q g(w) w q}} The reduction of s g(w) to equivalence classes is a partially ordered (transitive, reflexive, antisymmetric) set of degrees. The fact that Kratzer defines the order using the subset relation means that any two propositions that violate a disjoin set of norms will not be deontically or bouletically comparable. Image the ordering source g(w) gives two norms and the modal base contains two worlds (among others) as follows. (37) Two norms in g(w) a. Norm 1: There is no trespassing. 5

6 b. Norm 2: There is no murder. (38) Two worlds (among others) in the modal base a. w 1, where someone trespasses but no one commits murder b. w 2, where someone commits murder but no one trespasses Since w 1 violates Norm 1 but not Norm 2 and w 2 violates Norm 2 but not Norm 1, the two are deontically incomparable (neither w 1 g(w) w 2 nor w 2 g(w) w 1 ). If the modal base is rich enough and the propositions in the ordering source are logically independent, then Kratzer s theory predicts that neither (39a) nor (39b) will have a truth value. (39) a. It is better to trespass than it is to murder. b. It is better to murder than it is to trespass. It is also impossible to make any quantitative comparisons using Kratzer s theory. Kratzer s s g(w) is a pre-order. A Kratzer-structure K defined using this relation gives a very weak scale. For example, these structures are too weak to make sense of statements such as the following. (40) φ is much better than ψ. No matter how small the difference between the goodness of φ and ψ must be for φ to count as much better, there will be an admissible measure function for which the difference between φ and ψ fails to exceed this threshold. 5 Deontic conflicts Suppose you have promised to pick up your sister from the airport and you have promised to attend a concert with your friend. Now you learn that your sister is arriving during the concert. You have a deontic conflict. You ought to fulfill your promises, so you ought to pick up your sister from the airport and you ought to attend the concert. But you can t do both. On standard quantificational theories, such conflicts cannot exist. Suppose that ought A is true iff some world satisfying A is better than any world satisfying not A. Assume that A and B are incompatible. Thus, all worlds that satisfy B satisfy not A. Assume that it ought to be the case that A. Then some world satisfying A is better than any world satisfying B. But then it is not the cause that ought B. Either it ought to be the case that A or it ought to be the case that B or the two are incomparable. Kratzer s theory avoids this problem, but has a different one. When you make a promise, it is added to your ordering source g(w). When there is an inconsistency in the ordering source, there is no contradiction. However, it is still not possible for ought φ and ought ψ to be true if φ and ψ are inconsistent, since it is not the case that in all the undominated worlds it s the case that φ or in all the undominated worlds it s the case that ψ. (41) a. It s not the case that you should pick up your sister. w BEST(f(w))(g(w)) : w φ b. It s not the case that you should go to your friend s concert. w BEST(f(w))(g(w)) : w ψ This is the wrong prediction. What we want to say is that you should pick up your sister and you should go to your friend s concert. 6

7 References Cariani, F. (2013). Ought and resolution semantics. Noûs, 47(3): Charlow, N. (2013). What we know and what to do. Synthese, 190(12): Horn, L. (1989). A natural history of negation. University of Chicago Press, Chicago, Ill. Jackson, F. (1985). On the semantics of logic and obligation. Mind, 94(374): Jackson, F. and Pargetter, R. (1986). Oughts, options, and actualism. Philosophical Review, 9(2): Kolodny, N. and MacFarlane, J. (2010). Ifs and oughts. The Journal of Philosophy, 107(3): Kratzer, A. (1991). The representation of focus. In Stechow, A. v. and Wunderlich, D., editors, Semantics: An international handbook of contemporary research, pages Walter de Gruyter, Berlin. Ross, A. (1944). Imperatives and logic. Philosophy of Science, 11(1): von Fintel, K. and Iatridou, S. (2008). How to say ought in foreign: The composition of weak necessity modals. In Gueron, J. and Lecarme, J., editors, Time and Modality, pages Springer. 7